Image Noise Parameter Estimation by Principal Component Analysis

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Abstract

Noise parameter estimation is an important image processing step, because the noise parameters are often unknown, but many image denoising, compression, and segmentation algorithms take them as input values. The innovation of this thesis is the introduction of a new noise parameter estimation framework. The framework is designed to handle images with signal-independent noise as well as several common types of signal-dependent noise, namely, noise produced by synthetic aperture radars (SAR), magnetic resonance imaging (MRI) devices, charge-coupled device (CCD) sensors, and ultrasound devices.

The framework is based on a sparse representation of the blocks of the original image. Specifically, it is assumed that a part of the original image blocks lies in a proper subspace of the image block vector space, which means that there is a linear dependence between pixels in the blocks. As a result, images without homogeneous areas can be accurately processed, which is a qualitative difference from the state of the art, where homogeneous areas are required to process images with signal-dependent noise with several parameters.

In the case of signal-independent noise, principal component analysis of the blocks of the input image is utilized in order to check the sparsity assumption and estimate the noise variance. Particularly, Bartlett's test and the difference of the sample covariance matrix eigenvalues are used as assumption checks, and the last several sample covariance matrix eigenvalues are utilized to estimate the noise variance. Besides, two strategies to select the part of the blocks, which allows the sparse representation, are suggested.

In order to process images with signal-dependent noise, a variance-stabilizing transformation is applied. An optimization procedure is used to compute the transformation parameters, because they depend on the unknown noise parameters. This procedure analyzes the noise distribution in the transformed image and selects the transformation parameters, which maximize a noise normality measure. After applying the variance-stabilizing transformation, the algorithm designed for signal-independent noise is utilized to estimate the noise variance in the transformed image; and the parameters of the original noise model are calculated.

The noise parameter estimation experiments, which include comparison with 19 state of the art methods, show that the accuracy of the proposed algorithms is the highest in most cases. Speaking of signal-independent noise, the proposed algorithm gives a good compromise between accuracy and execution time: it is at least 15 times faster compared with the methods with similar accuracy; and it is at least 2 times more accurate than other methods. Regarding signal-dependent noise, the accuracy of the proposed approach is considerably higher for the SAR, CCD, and ultrasound noise models. The denoising experiments demonstrate that the use of noise parameter estimates computed by the proposed method results in considerably higher denoising quality for these three noise models.